The present invention relates generally to two- and three-dimensional mesh shapes and, more particularly, to the smoothing of the meshes on the surfaces of such shapes.
Many applications, such as medical and industrial design and manufacturing applications, involve manipulating and editing a digital model of an object. As one skilled in the art will understand, such a digital model may be created by scanning an object to create a point cloud representation of the object. The surface of such a model of a scanned object typically consists of a plurality of points, the number of which is a function of the resolution of the scanning process. Once such a point cloud representation has been obtained, the surface of the object may then be approximated by connecting the points of the point cloud to form a plurality of geometric shapes, such as triangles, on the surface of the model. This model may then, for example, be edited by using computer aided design (CAD) software programs or similar specialized image manipulation software programs.
FIG. 1 shows an illustrative model of the surface 101 of such an object. Referring to that figure, points 103 are, illustratively, the points in a point cloud that are obtained from the scanning of the object. Then, as discussed above, well-known methods are used to connect the points in a way such that the surface of the object is approximated by a plurality of triangles 102, referred to herein collectively as a triangle mesh. One such method for constructing a surface by connecting points and forming triangles is described, for example, in F. Bernardini et al., The Ball-Pivoting Algorithm for Surface Reconstruction, IEEE Transactions on Visualization and Computer Graphics, 5(4), October-December, 1999, pp. 349-359, which is hereby incorporated by reference herein in its entirety. Many other methods for creating mesh surfaces have also been developed and are well-known. As one skilled in the art will recognize, mesh surfaces created according to such prior methods contain noise caused by, for example, the scanning process and/or the mesh-creation process. When such noise is present, the model of an object may appear bumpy or may otherwise deviate from the actual appearance of the object scanned to create the model.
In order to correct for such noise in models, various smoothing operations have been performed on meshes to create more accurate models of surfaces. Such smoothing operations are well-known and typically include either geometric or signal processing methods. As is well known, geometric methods typically use discrete approximation to move mesh vertex points by, for example, weighting and averaging the position of each mesh vertex point with the points of nearby neighboring points to smooth the model of a surface. Signal processing methods, on the other hand, use various processing techniques, such as well-known isotropic or anisotropic filtering, to smooth a mesh surface.